The elevation of a landscape is modeled by a cubic function y=f(x)y = f(x)y=f(x), where y y\,y is the height in meters and x x\,x is the horizontal distance from a fixed point. A sketch of the curve y=f(x)y = f(x)y=f(x) shows that it starts from the bottom-left, rises to a local maximum, passes through the yyy-axis at (0,4)(0, 4)(0,4), and then descends to touch the xxx-axis at a local minimum point (3,0)(3, 0)(3,0) before rising again. The curve also intersects the xxx-axis at the point (−5,0)(-5, 0)(−5,0).
On separate diagrams, sketch the curve with equation:
y=f(x−5)y = f(x - 5)y=f(x−5)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
y=f(−12x)\displaystyle y = f\left(-\frac{1}{2}x\right)y=f(−21x)
On each diagram, show clearly the coordinates of all the points where the curve cuts or touches the coordinate axes.
33 exam-style questions on OCR (MEI) A Level Maths 1.4 Graphs, covering 1.4.1 Graphs of functions, 1.4.2 Intersection points with axes, 1.4.3 Completing the square for a quadratic curve, 1.4.4 Sketch graphs of simple functions, 1.4.5 Stationary points when curve sketching, 1.4.6 Graphs of reciprocal-type functions, 1.4.7 Single transformations of graphs, 1.4.8 Combined transformations of graphs (A-level only), and 1.4.9 Stationary points of inflection (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.